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4.2.10 Voltage/Current-Controlled Sources Four types of controlled sources are available: - Voltage controlled voltage source VVCVS - Current controlled voltage source VCCVS/VCCVS_1 - Vo

4.2.10 Voltage/Current-Controlled Sources

Four types of controlled sources are available:

- Voltage controlled voltage source (VVCVS)

- Current controlled voltage source (VCCVS/VCCVS_1)

- Voltage controlled current source (IVCCS)

- Current controlled current source (ICCCS/ICCCS_1)

- Variable-gain voltage controlled voltage source (VVCVSV)

- Variable-gain voltage controlled current source (IVCCSV)

For current controlled voltage/current source (VCCVS/ICCCS), the controlling current must come from a RLC branch Also, for a controlled current source, the controlling volt-age/current can not be an independent source

Note that voltage/current-controlled sources can be used in the power circuit only

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For voltage-controlled sources VVCVS/IVCCS, the controlling voltage is from the posi-tive node (+) to the negaposi-tive node (-) For current-controlled sources VCCVS/ICCCS, the control nodes are connected across a RLC branch, and the direction of the controlling cur-rent is indicated by the arrow For curcur-rent-controlled sources VCCVS_1/ICCCS_1, the controlling current flows into one control node and out of the other A 10-uOhm resistor is used to sense the controlling current

For variable-gain controlled voltage/current sources, Input 1 is on the side with the multi-plication sign, and Input 2 is on the side with the letter “k”

For the controlled voltage/current sources, the output is equal to the gain multiplied by the controlling voltage or current, respectively For the variable-gain controlled voltage/cur-rent sources, however, the output is equal to the following:

v in1 v in2 v in1 v in2

v o = (k v⋅ in2)⋅v in1

The difference between the variable-gain controlled sources and the nonlinear sources VNONM/INONM described in the following section is that for VNONM/INONM, values

of both v in1 and v in2 at the current time step are used to calculate the output and are updated in each iteration But for the variable-gain controlled sources, it is assumed that

the change of v in2 is small from one time step to the next, and the value of v in2 at the

previ-ous time step is used at the current time step This assumption is valid as long as v in2 changes at a much slower rate as compared to v in1 and the time step is small as compared

to the change of v in2 The variable-gain controlled sources can be used in circuits which may otherwise have convergence problem with the nonlinear sources VNONM/INONM

Example:

The circuits below illustrates the use of the current controlled voltage sources VCCVS and VCCVS_1

In the circuit on the left, the voltage source VCCVS is controlled by the inductor current

i s With a gain of 1, the waveform of the voltage v is is identical to that of i s In this way, a current quantity can be converted to a voltage quantity

The circuit on the right is equivalent to that on the left, except that the source VCCVS_1 is used instead

4.2.11 Nonlinear Voltage-Controlled Sources

The output of a nonlinear voltage-controlled source is either the multiplication, division,

or square-root of the input voltage(s) They are defined as:

VNONM - Voltage source where INONM - Current source where

i o = (k v⋅ in2)⋅v in1

V is

i s

V is

i s

v o = k v⋅ in1⋅v in2

i o = k v⋅ in1⋅v in2

VNOND - Voltage source where

INOND - Current source where

VNONSQ - Voltage source where INONSQ - Current source where VPOWERS - Voltage source where

In VPOWERS, the term sign(v in ) is 1 if v in is positive, and it is -1 if v in is negative

Note that these nonlinear voltage-controlled sources can be used in the power circuit only

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For all the sources except VPOWERS:

For VPOWERS:

For VNOND/INOND, Input 1 is on the side of the division sign

Coefficient k 1 Coefficient k 1

Coefficient k 2 Coefficient k 2

v o k v in1

v in2

-⋅

=

i o k v in1

v in2

-⋅

=

v o = k⋅ v in1

i o = k⋅ v in1

v o = sign v( )in ⋅ ⋅k (k1⋅v in)k2

VPOWERS

4.3 Voltage/Current Sensors

Voltage/current sensors measure the voltages/currents of the power circuit and send the value to the control circuit The current sensor has an internal resistance of 1 µΩ

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Probes and meters are used to request a voltage, current, or power quantity to be dis-played The voltage probe (VP) measures a node voltage with respect to ground The two-terminal voltage probe (VP2) measures the voltage between two nodes The current probe (IP) measures the current through the probe Note that all the probes and meters, except the node-to-ground probe VP, are allowed in the power circuit only

While probes measure a voltage or current quantity in its true form, meters can be used to measure the dc or ac voltage/current, or the real power and reactive power These meters function in the same way as the actual meters

For the current probe, a small resistor of 1 µΩ is used internally to measure the current

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ISEN VSEN

Probes and Meters

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A low-pass filter is used in the dc meter and wattmeter models to filter out the high-fre-quency components, whereas a high-pass filter is used in the ac meter and VAR meter models to filter out the dc component The cut-off frequency determines the transient response of the filter

Except the voltage current probes (VP/VP2/IP), the readings of all the meters are mean-ingful only when the readings reach the steady state

For the single-phase VA-Power Factor meter, the apparent power (S), total power factor (PF), and the displacement power factor (DPF) are defined as follows

Operating Frequency Operating frequency, or fundamental frequency, in Hz, of

the ac meter Cut-off Frequency Cut-off frequency, in Hz, of the low-pass/high-pass filter

VA Display Flag Display flag for apparent power (0: no display; 1: display)

PF Display Flag Display flag for power factor (0: no display; 1: display) DPF Display Flag Display flag for displacement power factor (0: no display; 1:

display)

VP2

AC Voltmeter

Voltage Probe Current Probe

VA_PF

VA-Power Factor Meter

VA_PF3

3-phase VA-Power Factor Meter

Assume both the voltage and current contains harmonics, i.e.

where ω1 is the fundamental frequency and all others are harmonic frequencies We have the rms values of the voltage and current as:

The apparent power is defined as:

The real power (or average power) is defined as:

where T is the fundamental period The total power factor PF and the displacement power factor DPF are then defined as follow:

For the three-phase circuit, the definitions are similar Note that the meter VA_PF3 is for the 3-phase 3-wire circuit, and the summation of the three phase voltages or currents must

be equal to zero, that is:

4.5 Switch Controllers

A switch controller has the same function as a switch gate/base drive circuit in an actual circuit It receives the input from the control circuit, and controls the switches in the power circuit One switch controller can control multiple switches simultaneously

v t( ) = 2V1sin(ω1t+φ1)+ 2V2sin(ω2t+φ2)+

i t( ) = 2I1sin(ω1t+θ1)+ 2I2sin(ω2t+θ2)+

V rms = V12+V22+

I rms = I12+I22+

S = V rms⋅I rms

T

- (v t( )⋅i t( ))d t

0

T

∫

=

S

-=

DPF = cos(φ1–θ1)

v a+v b+v c = 0

i a+i b+i c = 0

Switch Controllers

4.5.1 On-Off Switch Controller

On-off switch controllers are used as the interface between the control gating signals and the power switches The input, which is a logic signal (either 0 or 1) from the control cir-cuit, is passed to the power circuit as the gating signal to control switches

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Example:

The circuit below implements the step change of a load In the circuit, the on-off switch controller is used to control the bi-directional switch The step voltage source, which is connected to the controller input, changes from 0 to 1 at the time of 12 ms The closure of the switch results in the short-circuit of the resistor across the switch and the increase of the current

4.5.2 Alpha Controller

The alpha controller is used for delay angle control of thyristor switches or bridges There are three input for the controller: the alpha value, the synchronization signal, and the gat-ing enable/disable signal The transition of the synchronization signal from low to high (from 0 to 1) provides the synchronization and this moment corresponds to when the delay angle alpha equals zero A gating with a delay of alpha degrees is generated and sent to the thyristors The alpha value is updated instantaneously

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ONCTRL

On-off Controller

The input for the delay angle alpha is in deg

Example:

The figure below shows a thyristor circuit using delay angle control In the circuit, the

zero-crossing of v s, which corresponds to the moment that the thyristor would start con-ducting naturally, is used to provide the synchronization The delay angle is set at 30o The gating signal is delayed from the rising edge of the synchronization signal by 30o

4.5.3 PWM Lookup Table Controller

There are four input signals in PWM lookup table controllers: the modulation index, the delay angle, the synchronization signal, and the gating enable/disable signal The gating pattern is selected based on the modulation index The synchronization signal provides the synchronization to the gating pattern The gating pattern is updated when the synchroniza-tion signal changes from low to high The delay angle defines the relative angle between the gating pattern and the synchronization signal For example, if the delay angle is 10

Frequency Operating frequency of the controlled switch/switch

module, in Hz Pulse Width On-time pulse width of the switch gating, in deg

ACTRL

Enable/Disable

Alpha Sync.

Signal

v s

v sync

i RL1

Switch Controllers

deg., the gating pattern will be leading the synchronization signal by 10 deg

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A lookup table, which is stored in a file, contains the gating patterns It has the following format:

n, m1, m2, , m n

k1

G1,1, G1,2, , G 1,k1

k n

G n,1 , G n,2 , , G n,kn

where n is the number of gating patterns; m i is the modulation index correspondent to

Pat-tern i; and k i is the number of switching points in Pattern i The modulation index array m1

to m n should be monotonically increasing The output will select the ith pattern if the input

is smaller than or equal to m i If the input exceeds m n, the last pattern will be selected

The following table shows an example of a PWM pattern file with five modulation index levels and 14 switching points

5, 0.901, 0.910253, 0.920214, 1.199442, 1.21 14

7.736627 72.10303 80.79825 99.20176 107.8970 172.2634 180 187.7366 252.1030 260.7982 279.2018 287.8970 352.2634 360

Frequency Switching frequency, in Hz

Update Angle Update angle, in deg., based on which the gatings are

internally updated If the angle is 360o, the gatings are updated at every cycle If it is 60o, the gatings are updated at every 60o

File Name Name of the file storing the PWM gating pattern

PATTCTRL

Enable/Disable

Mod

Index Sync.

Delay

Signal Angle

14 7.821098 72.27710 80.72750 99.27251 107.7229 172.1789 180 187.8211 252.2771 260.7275 279.2725 287.7229 352.1789 360 14

7.902047 72.44823 80.66083 99.33917 107.5518 172.0979 180 187.9021 252.4482 260.6608 279.3392 287.5518 352.0980 360 14

10.186691 87.24225 88.75861 91.24139 92.75775 169.8133 180 190.1867 267.2422 268.7586 271.2414 272.7578 349.8133 360 14

10.189426 87.47009 88.97936 91.02065 92.52991 169.8106 180 190.1894 267.4701 268.9793 271.0207 272.5299 349.8106 360

In this example, if the modulation index input is 0.8, the output will select the first gating pattern If the modulation index is 0.915, the output will select the third pattern

Example:

This example shows a three-phase voltage source inverter (file: “vsi3pwm.sch”) The PWM for the converter uses the selected harmonic elimination The gating patterns are described above and are pre-stored in File “vsi3pwm.tbl” The gating pattern is selected based on the modulation index The waveforms of the line-to-line voltage and the three-phase load currents are shown below

A switch controller has the same function as a switch gate/base drive circuit in an actual circuit It receives the input from the control circuit, and controls the switches in the power circuit One switch controller can control multiple switches simultaneously

Function Blocks

4.6.1 Control-Power Interface Block

A control-power interface block passes a control circuit value to the power circuit It is used as a buffer between the control and the power circuit The output of the interface block is treated as a constant voltage source when the power circuit is solved With this block, some of the functions that can only be generated in the control circuit can be passed

to the power circuit

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Example: A Constant-Power Load Model

For a constant-power dc load, the voltage V, current I, and power P have the relationship

as P=V*I Given the voltage and the power, the current can be calculated as I=P/V This

can be implemented using the circuit as shown below

The load voltage is measured through a voltage sensor and is fed to a divider The output

of the divider gives the current value I Since the voltage could be zero or a low value at

the initial stage, a limiter is used to limit the current amplitude This value is converted into the load current quantity through a voltage-controlled current source

Example:

The following circuit illustrates how a control circuit signal can be passed to the power circuit As seen from the power circuit, the CTOP block behaviors as a grounded voltage source

CTOP

P

I V

k=1

LOAD

4.6.2 ABC-DQO Transformation Block

Function blocks ABC2DQO and DQO2ABC perform the abc-dqo transformation They convert three voltage quantities from one coordinate system to another These blocks can

be used in either the power circuit or the control circuit

It should be noted that, in the power circuit, currents must first be converted into voltage quantities (using current-controlled voltage sources) before they can be transformed The transformation equations from abc to dqo are:

The transformation equations from dqo to abc are:

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v d

v q

v o

2 3

-θ

3 -–

3 -+

cos

θ

3 -–

3 -+

sin 1

2

2

2

-v a

v b

v c

=

v a

v b

v c

θ

3 -–

3 -–

3 -+

3 -+

v d

v q

v o

⋅

=

Function Blocks

Example:

In this example, three symmetrical ac waveforms are transformed into dqo quantities The angle θ is defined as θ=ωt where ω=2π*60 Since the angle θ changes linearly with time,

a piecewise linear voltage which has a ramp waveform is used to represent θ The simula-tion waveforms show the three-phase ac (top), the angle θ (middle), and the dqo output In this example, the “q” component is constant, and both the “d” and the “o” components are zero

4.6.3 Math Function Blocks

The output of a math function block is expressed as the mathematical function of the inputs With this block, one can implement complex and nonlinear relationship easily and conveniently Blocks with 1, 2, 3, 5, and 10 inputs are provided

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